Retinal location of the preferred retinal locus relative to the fovea in scanning laser ophthalmoscope images.

Abstract

It is difficult to determine the position of a preferred retinal locus (PRL) relative to the fovea in scanning laser ophthalmoscope (SLO) images as a result of disease-related retinal morphologic changes that obscure the fovea. To overcome this problem, we developed a method for determining retinal foveal position based on normal fixation position relative to the optic disk. The normal foveal position measurements can then be used to estimate the distance between a PRL and the fovea.
Using the SLO, foveal position was determined for 50 normal subjects by measuring the retinal locus of fixation relative to the optic disk in undistorted SLO images. The resulting normal foveal fixation area is described by a bivariate normal ellipse that can be plotted on any undistorted SLO image. Measurement reliability was assessed by repeated measurements. The PRL relative to the normal foveal fixation area was determined for 24 subjects with macular degeneration and bilateral central scotomas.
The normal foveal fixation area based on all 50 subjects is described by a p = 0.9 bivariate ellipse whose centroid is located 12.6 degrees temporal to the temporal optic disk edge and 1.4 degrees inferior to a horizontal line bisecting the disk. PRL area is shown to increase with distance from the foveal fixation ellipse centroid. The shape of the PRL, characterized by the ratio of PRL ellipse major to minor axis, was found to depend on whether the PRL was vertically or horizontally aligned with the foveal fixation centroid.
PRL position relative to the fovea can be reliably estimated by plotting the normal foveal fixation bivariate ellipse on undistorted SLO images of retinas in which the fovea is obscured as a result of the disease process.

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ORIGINAL ARTICLES
Retinal Location of the Preferred Retinal Locus
Relative to the Fovea in Scanning Laser
Ophthalmoscope Images
GEORGE T. TIMBERLAKE, PhD, MANOJ K. SHARMA, MD, SUSAN A. GROSE, BS,
DENISE V. GOBERT, PT, PhD, JOHN M. GAUCH, PhD, and JOSEPH H. MAINO, OD, FAAO
Kansas City Veterans Affairs Medical Center, Kansas City, Missouri (GTT, MKS, SAG, DVG, JHM); Department of Ophthalmology,
University of Kansas Medical Center, Kansas City, Kansas (GTT, JHM); Department of Electrical Engineering and Computer Science,
University of Kansas, Lawrence, Kansas (JMG)
ABSTRACT: Purpose: It is difficult to determine the position of a preferred retinal locus (PRL) relative to the fovea in
scanning laser ophthalmoscope (SLO) images as a result of disease-related retinal morphologic changes that obscure the
fovea. To overcome this problem, we developed a method for determining retinal foveal position based on normal
fixation position relative to the optic disk. The normal foveal position measurements can then be used to estimate the
distance between a PRL and the fovea. Methods: Using the SLO, foveal position was determined for 50 normal subjects
by measuring the retinal locus of fixation relative to the optic disk in undistorted SLO images. The resulting normal
foveal fixation area is described by a bivariate normal ellipse that can be plotted on any undistorted SLO image.
Measurement reliability was assessed by repeated measurements. The PRL relative to the normal foveal fixation area
was determined for 24 subjects with macular degeneration and bilateral central scotomas. Results: The normal foveal
fixation area based on all 50 subjects is described by a p ? 0.9 bivariate ellipse whose centroid is located 12.6° temporal
to the temporal optic disk edge and 1.4° inferior to a horizontal line bisecting the disk. PRL area is shown to increase
with distance from the foveal fixation ellipse centroid. The shape of the PRL, characterized by the ratio of PRL ellipse
major to minor axis, was found to depend on whether the PRL was vertically or horizontally aligned with the foveal
fixation centroid. Conclusions: PRL position relative to the fovea can be reliably estimated by plotting the normal foveal
fixation bivariate ellipse on undistorted SLO images of retinas in which the fovea is obscured as a result of the disease
process. (Optom Vis Sci 2005;82:E177)
Key Words: preferred retinal locus, PRL, fixation, optic disk, retinal function mapping, scanning laser
ophthalmoscope, SLO, bivariate normal ellipse
I
scure landmarks such as perifoveal capillaries or macular pigment
that ordinarily allow determination of foveal position. Conse-
quently, many investigators have reported the location of the pre-
ferred retinal locus (PRL) of fixation relative to the macular sco-
toma rather than the fovea.1, 2It would be useful, however, to
know PRL location relative to the fovea because many aspects of
visual function vary with distance from the fovea, not necessarily
position relative to a scotoma. Fortunately, the optic disk often
remains relatively unaffected in macular disease and hence may
afford a landmark by which to locate the fovea.
dentifying and locating the fovea in scanning laser ophthalmo-
scope (SLO) images of retinas with macular degeneration is
difficult or impossible because the disease process tends to ob-
The position of the fovea relative to the optic disk has been
measured anatomically from postmortem eyes,3, 4from fundus
photographs,5and by visual field perimetry.6It is difficult, how-
ever, to use these measurements to specify accurately foveal posi-
tion in SLO images. Using the SLO, Timberlake et al.7estimated
foveal position in subjects with macular disease by fitting lines to
small-caliber blood vessels near the fovea, but did not measure the
distances from the estimated foveal position to the optic disk.
Rohrschneideretal.8, 9performedextensiveSLOmeasurementsof
foveal position relative to the optic disk center in normal subjects,
butconcludedthatthemeasurementswerenotadequatefordeter-
mining foveal location in eyes with morphologic changes.
We describe a method for measuring foveal location relative to
1040-5488/05/8203-0177/0 VOL. 82, NO. 3, PP. E177
OPTOMETRY AND VISION SCIENCE
Copyright © 2005 American Academy of Optometry
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the optic disk based on SLO measurements of normal fixation and
describe the reliability of the SLO measurements. Our methodol-
ogy is somewhat similar to that described by Rohrschneider et al.,8
but we characterize foveal location by a bivariate normal ellipse
enclosing mean fixation positions relative to the optic disk of nor-
mal subjects in undistorted SLO images. The bivariate ellipse, in
turn, allows estimation of the error with which foveal location can
be specified. The estimate of normal foveal position relative to the
optic disk can be plotted on undistorted SLO images of retinas
withmaculardisease,allowingdeterminationofthedistanceofthe
fovea to the PRL. The mathematics of the bivariate normal ellipse
is described in the Appendix because there has been no previous
detailed treatment of this topic in the literature on fixational eye
movements.
MATERIALS AND METHODS
Subjects
Participants included 50 normal subjects (21 to 65 years old)
who reported having normal vision as well as 24 subjects (67 to 89
yearsold)withmaculardegenerationandcentralscotomasinboth
eyes. All subjects provided written, informed consent approved by
the Kansas City Veterans Affairs Medical Center Human Subjects
Committee.
Procedure
Subjects stabilized their heads on the Rodenstock SLO chin/
forehead rest and fixated with the right eye a small red cross or
square presented in the SLO laser-beam raster. The subject’s left
eye was patched. Subjects were not explicitly corrected to em-
metropia. The examiner moved the fixation cross until the sub-
ject’s optic disk was fully visible in the SLO image. Subjects were
instructed to “look as closely as possible at the center of the cross
(or square), just as if you were trying to look at a very small object
far away.” The experimenter counted aloud to 10 for each 10-s
fixation trial. Between trials, subjects were asked to blink and then
refixate the target. Three trials were conducted for each subject.
SLO images were continuously videotaped.
Image Processing and Measurement.
Videotaped SLO images of fixation were digitized at 10 frames/
secusinganOspreydigitizingboard(ViewCastCorp.,Dallas,TX)
and software that converted the images from .avi to .jpg format.
Images were digitized at half-size (305 by 188 pixels) for conve-
nience of storage and processing. All digitized SLO images were
rotated so that they were equivalent to a projection of the retina
onto the visual field. Thus, superior retina is on the bottom of the
image and nasal retina is on the right for right eyes. This orienta-
tion is used here in all SLO figures.
For each subject, one digitized frame was selected for measure-
ment of the optic disk edge, a retinal vessel landmark, and fixation
stimuluslocation(Fig.1).TheX-Ycoordinatesoftheselandmarks
(inpixels)werethenusedinsubsequentcalculations.Todefinethe
temporal edge of the optic disk, the measurer used Photoshop
(Adobe Systems, Inc., Seattle, WA) to place lines at the nasal,
temporal, superior, and inferior borders of the disk, forming a box
around the optic disk (Fig. 1). A fifth, horizontal line was then
placed so it bisected the box surrounding the disk. The horizontal
bisecting line and the vertical line defining the temporal disk edge
wereusedasthediskcoordinate(AinFig.1).TheX-Ycoordinates
of a retinal vessel landmark (crossing or bifurcation) and the fixa-
tion stimulus were then recorded.
Tocharacterizethenormalretinallocusofthefixationstimulus,
the retinal landmark (B in Fig. 1) must be measured on multiple
SLO video frames during fixation. There were 50 subjects, each
with 100 0.1-s video frames per fixation, resulting in 5000 poten-
tial manual measurements of the retinal landmarks. To limit the
measurements to a manageable number, we determined how the
estimate of the mean fixation location and its standard deviation
(SD) varied with the number of samples. To this end, the vessel
FIGURE 1.
Illustration of scanning laser ophthalmoscope image measurements made for each subject. (A) Optic disk coordinate at temporal edge of disk. (B) Retinal
vessel landmark measured on all images. (C) Cross marks the center of the square fixation stimulus.
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landmark was measured on all 100 frames of one 10-s fixation for
five arbitrarily selected subjects. The mean fixation position (in
pixels) and X and Y standard deviations (in pixels) were then cal-
culated. The 100 samples were then resampled at 0.2, 0.3, 0.4,
. . .1.0 s (i.e., every second, third, fourth, and so on, sample of the
original100).Meansandstandarddeviationswereagaincalculated
for each sample interval. The results of this analysis are shown in
Fig. 2. The mean and SD increase with decreasing numbers of
samples but remain within 5% of the 100-sample results when 20
samples are used (i.e., 0.5 s between video frames). We considered
this a reasonable trade-off between accuracy and the time required
for analysis, and consequently, all subsequent measurements of
normal subjects’ fixation were made from 20 video frames of one
fixation trial (i.e., every 0.5 s for 10 s). The 10-Hz digitization rate
was selected because it provided a sufficient number of frames for
measuring retinal position of the fixation stimulus every 0.5 s (for
normal subjects) or every 0.3 s (for PRL subjects, see below), even
when frames that contained saccades or that were obscured by
blinks were eliminated from measurement. Measurements of the
retinal vessel landmark were made using Inspector software (Ma-
trox Electronic Systems, Ltd., Dorval, Québec) by selecting every
fifthSLOvideoframefromthesetof100.TheresultingarrayofX,
Y coordinates were stored for later use by MatLab (The Math-
Works, Inc., Natick, MA) programs.
To characterize PRL fixation of subjects with macular degener-
ation and central scotomas, digitized SLO images were sampled
approximately every third frame over the three 10-s fixation trials
(i.e., position was sampled every 0.3 s for 30 s) to give 100 fixation
measurementspersubject.PRLfixationwasmoreextensivelysam-
pled than normal fixation as a result of the large variability of
retinal fixation position in PRL’s.
Undistorting Scanning Laser Ophthalmoscope
Measurements and Images
Rodenstock SLO images are trapezoidally distorted from top to
bottom by approximately 10%.10Consequently, the optic disk,
fixation point, and vessel landmark coordinates described above
need to be undistorted. We performed this undistortion mathe-
matically using MatLab programs. Images for plotting the retinal
locus of fixation (foveal or PRL) were undistorted using an inter-
polation algorithm that reshaped the distorted image to its true
shape (Fig. 3). (The computer program for undistorting SLO im-
ages using an interpolation algorithm can be found at www.ittc.
ku.edu/?jgauch.) After undistortion, the optic disk was outlined
as described previously, and the disk coordinate was measured. As
described previously the plotting image is oriented as a projection
of the retina onto the visual field (i.e., superior retina on the bot-
tom and nasal retina on the right).
Measurement Repeatability
The optic disk and landmark measurements described here are
associated with uncertainties because these features are not always
clear in SLO images. This is particularly true of the optic disk that
can have unclear or “fuzzy” borders. Consequently, different mea-
surers may select different positions for the lines that outline the
disk and define the temporal disk coordinate. The retinal vessel
landmark can also vary in quality from frame to frame, making
measurement uncertain. To assess the error produced by these
measurement uncertainties, we performed three sets of measure-
ments. First, three of the authors independently measured the
optic disk, a vessel landmark of their choosing, and the fixation
point from 20 images of each of 25 normal subjects. Second, three
of the authors independently measured the optic disk edge coor-
dinate for another set of 25 normal subjects. Third, two of the
authorsmeasuredaretinalvessellandmarkfivetimesforeachof20
video frames of two subjects. The order of measurements was ran-
domized between each set of 20 frames. Of the two subjects mea-
sured,onehadaveryclearlydefinedretinalvesselcrossing,whereas
the other had a less sharp vessel crossing that appeared “fuzzy” or
indistinct in some video frames.
Calculation of Fixation Position
For each normal subject, fixation position relative to the optic
disk was calculated as the mean horizontal (X) and vertical (Y)
fixation stimulus positions measured in the 20 sampled SLO
frames. The ensemble of mean fixation positions relative to the
optic disk of all 50 normal subjects was characterized using
FIGURE 2.
Effect of scanning laser ophthalmoscope video frame sampling interval on estimate of the mean and standard deviation (SD) of fixation location of five
normal subjects. (A) Percentage change in mean X and Y fixation position with decreasing numbers of samples. (B) Percentage change in X and Y SD’s
with decreasing sample number. Horizontal line in plots ? 5%.
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the bivariate normal ellipse. Major and minor ellipse axes and the
mean fixation position were calculated using MatLab programs.
The bivariate normal ellipse area was calculated using the
relationship
A ? ??2?x?y?1 ? ?2
whereAisthearea(deg2orminarc2),?2isthechi-squaredvalue
(2 df) corresponding to a probability of 0.9, ?xand ?yare the
standard deviations in X and Y, and ? is the Pearson product
moment correlation coefficient (see Appendix). Bivariate normal
ellipses were also used to characterize PRL fixation.
RESULTS
Normal Foveal Fixation
An example of the retinal fixation locus of one ocularly normal
subject is shown in Fig. 4. Individual fixation measurements were
dispersed five pixels horizontally and seven pixels vertically (Fig. 4,
inset). The mean fixation position based on these measurements
(Fig.4,largewhitedot)was11.9°temporaltothetemporaledgeof
the optic disk and 1.4° inferior to a horizontal line bisecting the
disk as described previously.
Normal fixation was somewhat more variable in the horizontal
directionthanintheverticaldirection(Fig.5).Standarddeviations
ofretinalfixationtargetpositionrangedfrom4to32minarcinthe
horizontal direction (Fig. 5A) as compared with a 4 to 18 min arc
intheverticaldirection(Fig.5B).MeanhorizontalfixationSDwas
8.84 min arc as compared with a 6.01 min arc for vertical.
Foveal Fixation Area of All Ocularly Normal
Subjects
Themeanfixationlocirelativetotheopticdiskofall50ocularly
normal subjects are shown in Fig. 6. The data are plotted on an
undistorted SLO retinal image of one of the subjects. Mean X and
Y fixation positions are normally distributed (Shapiro-Wilk Tests:
X: W ? 0.993, p ? 0.994, ? ? 0.05; Y: W ? 0.984, p ? 0.741,
??0.05).Twobivariatenormalellipsesareshownfortheensem-
bleof50subjects:theouterellipseisforp?0.9,whereastheinner
ellipseisforp?0.68.Themeanhorizontalfixationlocus(i.e.,the
ellipse centroid where the major and minor axes cross) is 12.6° ?
0.9°temporaltothetemporaledgeoftheopticdiskedgeand-1.4°
? 0.8° inferior to a horizontal line bisecting the disk. Individual
mean fixation loci ranged from 10.4° to 15.0° horizontally and
from -3.45° to 0.45° vertically. The ellipse major axis is tilted
somewhat inferior nasally. The fixation area is close to being cir-
cular (i.e., ratio of major to minor ellipse axes, Lmaj/Lmin? 1.20).
The area enclosed by the p ? 0.9 ellipse is 10.48 deg2and that
enclosed by the p ? 0.68 ellipse is 5.21 deg2. By comparison, the
area of the optic disk (assuming a diameter of 5 deg) is 19.6 deg.2
It is important to note that individual normal subjects’ fixation
bivariateellipseareasarequitesmallcomparedwiththeellipsethat
encloses the ensemble of all 50 mean fixation positions. For exam-
ple, the average individual p ? 0.68 bivariate ellipse area is about
400 min arc2(?0.1 deg2), about 1/50ththe size of the p ? 0.68
ellipse for all 50 mean fixation positions. Thus, individual fixation
bivariate ellipses would be about the size of the symbols used to
plot individual mean fixation positions in Fig. 6.
Retinal Location of the Preferred Retinal Locus
Relative to Foveal Position
Once the disk coordinate is measured, the bivariate normal fix-
ation ellipse shown in Fig. 6 can be plotted on any undistorted
SLO image that shows the subject’s optic disk clearly. In addition,
a subject’s PRL can be plotted on the same image because PRL
fixation points are measured in the same way as for normal sub-
jects.AnexampleofsuchaplotisshowninFig.7wheretheareaof
the p ? 0.9 PRL bivariate ellipse is 11.4 deg2. The PRL centroid
(Fig. 7) is offset temporally from the normal fixation ellipse cen-
troid by 2.6 deg and superiorly by 7.8 deg.
The same plotting process described above can be used to plot
multiple PRL’s and the normal fixation area on a single image. An
example of such multiple retinal PRL positions relative to the
normalfixationareaisshowninFig.8wherePRL’sof22ofthe24
FIGURE 3.
Example of undistorted scanning laser ophthalmoscope image used for
plotting fixation points. Arrow points to the disk edge coordinate.
FIGURE 4.
Undistorted scanning laser ophthalmoscope image showing mean retinal
fixation locus (large white dot) of an ocularly normal subject. Inset shows
expanded view of measured loci of fixation target (points overlap in some
instances). Text at bottom of image was added during videotape recording
and was not seen by the subject.
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scotoma subjects are shown (the remaining two PRL’s are outside
the image).
Fig. 8 suggests that PRL area increases with distance from the
foveal fixation area. This relationship is borne out as shown in Fig.
9 in which log PRL area for all 24 scotoma subjects is plotted as a
function of the distance of the PRL centroid to the foveal fixation
area centroid. PRL area is normally distributed after logarithmic
transformation (Shapiro-Wilk Test, W ? 0.93, p ? 0.134, ? ?
0.05).DistancefromthefovealfixationellipsecentroidtothePRL
centroid is also normally distributed (Shapiro-Wilk Test: W ?
0.969,p?0.657,??0.05).LogPRLareaispositivelycorrelated
with distance from the foveal fixation area (Pearson product mo-
ment correlation, r ? 0.63). This correlation is significantly dif-
ferent from zero (t ? 3.83, p ? 0.001).
Fig. 8 also suggests that PRL ellipses are more “flattened” (i.e.,
the ellipse is shorter vertically and longer horizontally) when they
are more horizontally aligned with the normal foveal fixation area
and more “circular” when more vertically aligned. This relation-
ship is borne out as shown in Fig. 10A where the PRL “shape” is
characterized by the ratio of the lengths of the major and minor
ellipse axes (Lmaj/Lmin). A circular PRL would have a ratio of 1.0,
whereas an elongated PRL would have a ratio ?1.0. PRL shape is
normally distributed after logarithmic transform (Shapiro-Wilk
Test: W ? 0.932, p ? 0.069, ? ? 0.05). PRL alignment with the
centroid of the normal foveal fixation ellipse was characterized by
determining the angle the PRL made with a vertical axis passing
through the fixation area centroid as illustrated in Fig. 10B. With
thisscheme,aPRLwhosecentroidlayonahorizontallinethrough
thenormalfixationareacentroidwouldhaveanangleof90deg.A
PRL whose centroid was on a vertical line through the normal
fixation area centroid would have an angle of 0 deg. The angle of
PRL alignment with respect to the foveal fixation ellipse centroid
was not normally distributed, nor was its log transform. However,
the logarithm of PRL shape is positively correlated with the angle
the PRL makes with normal foveal fixation (Spearman rank corre-
lation, rs? 0.78, p ? 0.0001).
FIGURE 6.
Plot of fixation loci of all 50 ocularly normal subjects relative to the optic
disk of one subject. Bivariate ellipses: outer ellipse, p ? 0.9; inner ellipse,
p ? 0.68
FIGURE 7.
Plot of normal fixation area based on 50 normal subjects (top ellipse) and
one scotoma subject’s preferred retinal locus (bottom ellipse). Both el-
lipses are p ? 0.9
FIGURE 5.
Distributions of fixation standard deviations (SD’s) for all normal subjects (n ? 50). (A) Horizontal fixation SD’s. Mean horizontal SD shown by vertical
line (8.8 min arc). (B) Vertical fixation SD’s. Mean vertical SD ? 6.0 min arc.
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Optometry and Vision Science, Vol. 82, No. 3, March 2005